1.

A cylinder having diameter 40 cm and height 70 cm contains 4/5th of water. If a cone having radius 18 cm and height equal to 3/4 time the height of the cylinder is dropped in the cylinder, how much water wil overflow from the cylinder?

Answer»

Solution :Here, diameter = 40 CM , `therefore` radius (r ) = 20 cm
h = 70 cm
The volume of the cylinder (ui.e. the volume of water)
`pir^2h`
`=(22)/7xx20xx20xx70`
`=88000cm^3`
The water is up to `4/5` th of the cylinder
`therefore1/5` th of the cylinder is WITHOUT water
`therefore88000xx1/5=17600cm^3` of water can be added to the cylinder to make it full of water `""...(1)`
The radius (R) of the cone = 18 cm
H of the cone `=3/4xx70=52.5 cm`
The volume of the cone `=1/3xx(22)/7xx18xx52.5`
`=22xx18xx18xx2.5`
`=17820cm^3""...(2)`
`therefore` the water OVERFLOWING = `(17820-17600)cm^3""...["From (2) and (1)"]`
`=220cm^3`
`220cm^3` of water will overflow


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